CN115442762B - Target tracking method based on distributed consistency filtering of wireless sensor network - Google Patents
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Abstract
A target tracking method based on distributed consistency filtering of a wireless sensor network comprises the following steps: establishing a continuous kinematic model for the motion condition of a moving target on the horizontal ground; establishing a system state equation and an observation equation of each sensor node; designing a corresponding distributed consistency filter according to the observed value of each sensor; giving a system autonomous error model and the gain of each filter, designing and solving a consistency coefficient through a matrix inequality; substituting the consistency coefficients of the filters to obtain real-time estimated values, and realizing the real-time consistency position tracking of each sensor on the moving target. The method and the device have high accuracy and instantaneity for estimating the position of the moving target in real time, and the algorithm can be well matched no matter what target is used, so that the requirement of target tracking is met.
Description
Technical Field
The invention relates to the technical field of wireless sensor network target tracking, in particular to a target tracking method based on distributed consistency filtering of a wireless sensor network.
Background
In a wireless sensor network, a plurality of sensor nodes observe the state of an observed object (such as the position, the moving speed and the like of the object), and obtain estimated values of the object state from observed values containing noise by using various state estimation algorithms. In order to improve the performance of state estimation of each node, the traditional method is to collect observation information or local estimation information of all nodes through a fusion center to perform information fusion processing. Among them, the centralized Kalman (Kalman) filtering algorithm is a classical approach based on fusion centers. However, due to limitations of network architecture and communication capacity, these fusion center-based algorithms require a lot of costs in routing, topology management, data transmission, etc., and the existence of the fusion center reduces the fault tolerance and reliability of the algorithm. Therefore, the design of the distributed filtering algorithm without the fusion center has very important significance in the target tracking application of the wireless sensor network.
The existing distributed filtering tracking algorithm is mainly a Kalman consistency filtering algorithm Kalman Consensus Filter (KCF), and the states of all nodes in the wireless sensor network tend to be consistent through information exchange among neighbor nodes and distributed weighted iteration. However, solving the consistency coefficient in the kalman consistency filter is still a difficult problem, and if the chosen consistency coefficient is too large, the estimation effect is poor, and the consistency effect is poor. Therefore, selecting a proper consistency coefficient is particularly important in a consistency filtering algorithm.
Disclosure of Invention
The invention aims to solve the problems in the prior art and provides a target tracking method based on distributed consistency filtering of a wireless sensor network.
The working principle of the invention is as follows: assuming that a moving target exists on the horizontal ground, firstly establishing a continuous kinematic model for the moving target, and simulating the actual moving condition; then consider the inaccuracy of the target model and the interference suffered by the measurement as disturbance signals formed by random disturbance; a plurality of wireless sensor networks for observing the positions of the moving targets; further adopting distributed consistency filtering to perform data fusion processing, and enabling a plurality of sensor nodes to agree on state estimation of a moving target.
The target tracking method based on the distributed consistency filtering of the wireless sensor network comprises the following specific steps:
1) And establishing a continuous kinematic model for the motion condition of the moving object on the horizontal ground.
2) And establishing a system state equation and an observation equation of each sensor node.
3) Each sensor's observation is used to design its corresponding distributed consistency filter.
4) And (3) giving a system autonomous error model and the gain of each filter, designing and solving a consistency coefficient through a matrix inequality.
5) Substituting the consistency coefficients of the filters to obtain real-time estimated values, and realizing the real-time consistency position tracking of each sensor on the moving target.
Further, in step 1), a continuous kinematic model is built for the motion of a moving object on level ground. The horizontal ground environment is established into a plane rectangular coordinate system, and thenTo represent the position of the moving object, where P x represents the abscissa of the object and P y represents the ordinate of the object.
Further, in step 2), a system state equation and an observation equation for each sensor node are established. According to the actual situation, a system state equation and an observation equation of each sensor node are established, and the method comprises the following steps:
(2.1) establishing a state equation of the system. The state equation of the system is:
x(k+1)＝Ax(k)+B0ω0(k) (1)
Where k represents the current discretization time, k+1 represents the next discretization time, the estimation target x represents the position of the object, x= [ P x Py]T,Px ] represents the abscissa of the object, P y represents the ordinate of the object, the superscript "T" represents the transpose of the matrix, a represents the state transition matrix of the estimation target x, ω 0 represents white noise with a mean of 0 and a variance of 1, and B 0 represents the input matrix of white noise ω 0.
(2.2) Establishing an observation equation for each sensor. The observation equation for the i-th sensor is:
zi(k)＝Hix(k)+D0;iω0(k) (2)
Where k represents the current discretization time, z i represents the observation vector of the i-th sensor, x represents the estimation target, H i represents the observation matrix of the estimation target of the i-th sensor, ω 0 represents white noise with a mean value of 0 and a variance of 1, and D 0;i represents the observation matrix of the white noise ω 0 of the i-th sensor.
Further, in step 3), each sensor's corresponding distributed consistency filter is designed based on its observations. Assuming that N sensors are present and that there are corresponding filters on each sensor, defining η represents the set of all sensors, η: = {1,... In distributed hybrid filtering, for the ith filter, it can receive not only the observations z i (k) from its own sensor, but also the observations of its neighboring sensorsDefinition η i represents the set of adjacent observations received by the ith sensor. J i is defined as the i-th sensor itself and all its neighbors.
When the target is tracked, the data transmission is performed in the wireless sensor network, and for the ith sensor, the ith sensor can receive the observation value of the adjacent sensor through the wireless sensor network, but the data can be lost due to disturbance in the transmission process. Assuming that all observations actually received by the ith sensor are noted as:
where k represents the discretization time, Representing all data actually received by the ith sensor,/>All neighboring sensor observations/>, representing the ith sensorWhether the data transmitted to the ith sensor is lost.
Designing a distributed consistency filter of each sensor:
where k represents the current discretization time and k+1 represents the next discretization time. A represents a state transition matrix of the estimation object x, Represents the estimated value of the estimated object x, Σ represents the accumulated sign, e represents the belonging sign, L i represents the filter gain of the ith sensor, η i represents the set of adjacent observations received by the ith sensor, J i is the ith sensor itself and all its neighbors,/>All neighboring sensor observations/>, representing the ith sensorWhether data transmitted to the ith sensor is lost, Φ ij (k) represents whether data transmitted to the ith sensor by the neighbor sensor observation z j (k) of the ith sensor is lost, and/>Representing the set of all observation matrices of the ith sensor,/>Indicating all data actually received by the ith sensor, and alpha is the consistency coefficient to be determined.
The function of the distributed consistency filter is to enable each sensor to estimate the targetAnd (3) converging, and realizing real-time consistency estimation of the moving target.
In step 4), a system autonomous error model and the gain of each filter are given, and the consistency coefficient is designed and solved through matrix inequality. Giving a system autonomous error model and the gain of each filter, designing and solving a consistency coefficient through matrix inequality, and specifically comprising the following steps:
(4.1) an autonomous error model of the system is given. The following autonomous error system models are obtained through (1), 2 and 4) respectively:
Where k represents the current discrete time and k+1 represents the next discrete time. e i represents the estimation object x and the corresponding estimation value Sigma represents an accumulated sign, E represents a sign, L i represents a filter gain of an ith sensor, eta i represents a set of adjacent observations received by the ith sensor, A represents a state transition matrix of an estimation object, B 0 represents an input matrix of white noise omega 0, omega 0 represents white noise with a mean value of 0 and a variance of 1,/>All neighboring sensor observations/>, representing the ith sensorWhether data transmitted to the ith sensor is lost, Φ ij (k) represents whether data transmitted to the ith sensor by the neighbor sensor observation z j (k) of the ith sensor is lost, and/>Representing the set of all observation matrices of the ith sensor,/>Representing the set of all white noise observation matrices of the ith node, and alpha is the undetermined consistency coefficient.
(4.2) An expression of the filter gain L i is given. Based on a system autonomous error model (5), an expression of a designed filter gain L i is given through a Kalman filtering algorithm:
Where k represents the current discretization time, a represents the state transition matrix of the estimation object, the superscript "-1" represents the inverse of the matrix, the superscript "T" represents the transpose of the matrix, B 0 represents the input matrix of white noise ω 0, Set of all observation matrices representing the ith node,/>Representing the set of all white noise observation matrices of the ith node,/>Representation/>O 0;i (k) and Λ i are both intermediate matrices.
(4.3) A diagonal matrix set form of intermediate variables O 0;i is given. Intermediate variable O 0;i represents the covariance form of the autonomous system error model (5), i.eGiven the diagonal matrix set form of intermediate variable O 0;i:
O0＝Diag{O0;i} (7)
wherein Diag represents a diagonal matrix form, and O 0;i is an intermediate matrix.
(4.4) Initial values of intermediate variable O 0 are given. When k=0, an initial value is given to intermediate variable O 0, i.e
O0(0)(8)
(4.5) Giving the value of the consistency coefficient α. Assigning a given value to a pending consistency coefficient alpha, i.e
α＝ε (9)
Where α is the coefficient of identity to be determined and ε represents a given value.
(4.6) The matrix inequality of the intermediate matrix O 0 is given. The intermediate matrix O 0 satisfies the following matrix inequality:
Thus, an intermediate matrix O 0 (1) is obtained:
Where k represents the current discretization time, k+1 represents the next discretization time, the superscript "T" represents the transpose of the matrix, the superscript "2" represents the square of the value, mu ij represents the mathematical expectation of Φ ij, O 0 is the intermediate matrix, And/>All are intermediate matrices related to alpha, which is the predetermined consistency coefficient.
(4.7) Solving the maximum value of the consistency coefficient alpha under the condition that all characteristic values of the intermediate matrix O 0 are larger than 0. Repeating the steps (4.5) and (4.6).
If k=t, all eigenvalues satisfying the matrix O 0 (T) are greater than 0, and the maximum value of the consistency coefficient α is solved, so as to obtain:
max(α)，eig{O0(T)}>0 (12)
Where α is a predetermined consistency coefficient, eig represents a eigenvalue of the matrix, and O 0 is an intermediate matrix.
Further, in step 5), the consistency coefficient of the filter is substituted to obtain a real-time estimated value, so that the real-time consistency position tracking of each sensor on the moving target is realized. Substituting the solved consistency coefficient alpha into a distributed consistency filter (4) to realize real-time consistency estimation of each sensor node on the moving target x.
According to the target tracking method based on the distributed consistency filtering of the wireless sensor network, which is designed by the invention, matrix inequality is solved through a dichotomy, and then consistency coefficients of the filter are solved, and the distributed consistency filter is constructed to realize the real-time consistency estimation of the coordinates of the moving object at multiple points under the condition of multiple sensor nodes.
The invention has the advantages that: the influence of the actual multiple sensors is considered, a system state equation and an observation equation are established for the target model, a designed distributed consistency filter is provided, and real-time consistency estimation is carried out on the position of the moving target. The estimation result can meet the precision and real-time requirements of practical application, and the algorithm can be well matched no matter what target is used, so that the requirement of target tracking is met.
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FIG. 1 is a topology of an experimental node of the invention
FIG. 2 is a graph showing the experimental effect of the present invention.
Detailed Description
In order to make the purposes, technical schemes and specific effects of the invention clearer, the technical scheme of the invention is further described below in combination with practical experimental data.
The invention provides a target tracking method based on distributed consistency filtering of a wireless sensor network. The working principle is as follows: assuming that a moving target exists on the horizontal ground, firstly establishing a continuous kinematic model for the moving target, and simulating the actual moving condition; then consider the inaccuracy of the target model and the interference suffered by the measurement as disturbance signals formed by random disturbance; a plurality of wireless sensor networks for observing the positions of the moving targets; further adopting distributed consistency filtering to perform data fusion processing, and enabling a plurality of sensor nodes to agree on state estimation of a moving target.
In order to evaluate the divergence between the different local state estimates, the following criteria are proposed:
Wherein, Representing the estimated value of the estimation object x.
The invention relates to a target tracking method based on distributed consistency filtering of a wireless sensor network, which comprises the following specific steps:
1) Establishing continuous kinematic model for motion condition of moving object on horizontal ground
2) Establishing a system state equation and an observation equation of each sensor node
3) Designing each sensor's corresponding distributed consistency filter based on its observations
4) Giving a system autonomous error model and the gain of each filter, designing and solving a consistency coefficient through matrix inequality
5) Substituting the consistency coefficients of the filters to obtain real-time estimated values, and realizing the real-time consistency position tracking of each sensor on the moving target.
In step 1), a continuous kinematic model is built for the motion of a moving object on a level ground. The horizontal ground environment is established into a plane rectangular coordinate system, and thenTo represent the position of the moving object, where P x represents the abscissa of the object and P y represents the ordinate of the object.
In step 2), a system state equation and an observation equation of each sensor node are established. According to the actual situation, a system state equation and an observation equation of each sensor node are established, and the method comprises the following steps:
(2.1) establishing a state equation of the system. The state equation of the system is:
x(k+1)＝Ax(k)+B0ω0(k) (1)
where k represents the current discretization time, k+1 represents the next discretization time, the estimation target x represents the position of the object, x= [ P x Py]T,Px ] represents the abscissa of the object, P y represents the ordinate of the object, the superscript "T" represents the transpose of the matrix, Representing the state transition matrix of the estimation object x, ω 0 represents white noise with a mean of 0 and a variance of 1,Representing the input matrix of white noise omega 0.
(2.2) Establishing an observation equation for each sensor. The observation equation for the i-th sensor is:
zi(k)＝Hix(k)+D0;iω0(k) (2)
Where k represents the current discretization time, z i represents the observation vector of the i-th sensor, x represents the estimation target, when i is an odd number, H i = [ 0.3.0.4 ] represents the observation matrix of the estimation target of the i-th sensor, when i is an even number, H i = [ 0.4.0.3 ] represents the observation matrix of the estimation target of the i-th sensor, ω 0 represents white noise with a mean value of 0 and variance of 1, when i is an odd number, D 0;i = [ 0.15.20 ] represents the observation matrix of the white noise ω 0 of the i-th sensor, when i is an odd number, D 0;i = [ 0.20.15 ] represents the observation matrix of the white noise ω 0 of the i-th sensor, and the superscript "T" represents the transpose of the matrix.
In step 3), a corresponding distributed consistency filter is designed according to the observed value of each sensor. Assuming that N sensors are present and that there are corresponding filters on each sensor, defining η represents the set of all sensors, η: = {1,... In distributed hybrid filtering, for the ith filter, it can receive not only the observations z i (k) from its own sensor, but also the observations of its neighboring sensorsDefinition η i represents the set of adjacent observations received by the ith sensor. J i is defined as the i-th sensor itself and all its neighbors.
When the target is tracked, the data transmission is performed in the wireless sensor network, and for the ith sensor, the ith sensor can receive the observation value of the adjacent sensor through the wireless sensor network, but the data can be lost due to disturbance in the transmission process. Assuming that all observations actually received by the ith sensor are noted as:
where k represents the discretization time, Representing all data actually received by the ith sensor,/>All neighboring sensor observations/>, representing the ith sensorWhether the data transmitted to the ith sensor is lost.
Designing a distributed consistency filter of each sensor:
Where k represents the current discretization time and k+1 represents the next discretization time.
Representing the state transition matrix of the estimation object x,/>Represents the estimated value of the estimated object x, Σ represents the accumulated sign, e represents the belonging sign, L i represents the filter gain of the ith sensor, η i represents the set of adjacent observations received by the ith sensor, J i is the ith sensor itself and all its neighbors,/>All neighboring sensor observations/>, representing the ith sensorWhether data transmitted to the ith sensor is lost, Φ ij (k) represents whether data transmitted to the ith sensor by the neighbor sensor observation z j (k) of the ith sensor is lost, and/>Representing the set of all observation matrices of the ith sensor,/>Indicating all data actually received by the ith sensor, and alpha is the consistency coefficient to be determined.
In the step 4), a system autonomous error model and the gain of each filter are given, and the consistency coefficient is designed and solved through matrix inequality. Giving a system autonomous error model and the gain of each filter, designing and solving a consistency coefficient through matrix inequality, and specifically comprising the following steps:
(4.1) an autonomous error model of the system is given. The following autonomous error system models are obtained through (1), 2 and 4) respectively:
Where k represents the current discrete time and k+1 represents the next discrete time. e i represents the estimation object x and the corresponding estimation value Sigma represents the accumulated sign, E represents the belonging sign, L i represents the filter gain of the ith sensor, eta i represents the set of adjacent observations received by the ith sensor,/>Representing the state transition matrix of the estimation object x,An input matrix representing white noise ω 0, ω 0 representing white noise with a mean of 0 and a variance of 1,/>All neighboring sensor observations/>, representing the ith sensorWhether data transmitted to the ith sensor is lost, Φ ij (k) represents whether data transmitted to the ith sensor by the neighbor sensor observation z j (k) of the ith sensor is lost, and/>Representing the set of all observation matrices of the ith sensor,/>Representing the set of all white noise observation matrices of the ith node, and alpha is the undetermined consistency coefficient.
(4.2) An expression of the filter gain L i is given. Based on a system autonomous error model (5), an expression of a designed filter gain L i is given through a Kalman filtering algorithm:
where k represents the current discretization moment, The state transition matrix representing the estimation target x, the superscript "-1" representing the inverse of the matrix, the superscript "T" representing the transpose of the matrix,/>Input matrix representing white noise omega 0,/>Set of all observation matrices representing the ith node,/>Representing the set of all white noise observation matrices of the ith node,/>Representation/>O 0;i (k) and Λ i are both intermediate matrices.
(4.3) A diagonal matrix set form of intermediate variables O 0;i is given. Intermediate variable O 0;i represents the covariance form of the autonomous system error model (5), i.eGiven the diagonal matrix set form of intermediate variable O 0;i:
O0＝Diag{O0;i} (7)
wherein Diag represents a diagonal matrix form, and O 0;i is an intermediate matrix.
(4.4) Initial values of intermediate variable O 0 are given. When k=0, an initial value is given to intermediate variable O 0, i.e
O0(0)(8)
(4.5) Giving the value of the consistency coefficient α. Assigning a given value to a pending consistency coefficient alpha, i.e
α＝ε (9)
Where α is the coefficient of identity to be determined and ε represents a given value.
(4.6) The matrix inequality of the intermediate matrix O 0 is given. The intermediate matrix O 0 satisfies the following matrix inequality:
Thus, an intermediate matrix O 0 (1) is obtained:
Where k represents the current discretization time, k+1 represents the next discretization time, the superscript "T" represents the transpose of the matrix, the superscript "2" represents the square of the value, mu ij represents the mathematical expectation of Φ ij, O 0 is the intermediate matrix, And/>All are intermediate matrices related to alpha, which is the predetermined consistency coefficient.
(4.7) Solving the maximum value of the consistency coefficient alpha under the condition that all characteristic values of the intermediate matrix O 0 are larger than 0. Repeating the steps (4.5) and (4.6).
If k=t, all eigenvalues satisfying the matrix O 0 (T) are greater than 0, and the maximum value of the consistency coefficient α is solved, so as to obtain:
max(α)＝0.092，eig{O0(T)}>0 (12)
Where α is a predetermined consistency coefficient, eig represents a eigenvalue of the matrix, and O 0 is an intermediate matrix.
And 5) substituting the consistency coefficient of the filter to obtain a real-time estimated value, and realizing the real-time consistency position tracking of each sensor on the moving target. Substituting the solved consistency coefficient alpha into a distributed consistency filter (4) to realize real-time consistency estimation of each sensor node on the moving target x.
According to the target tracking method based on the distributed consistency filtering of the wireless sensor network, which is designed by the invention, matrix inequality is solved through a dichotomy, and then consistency coefficients of the filter are solved, and the distributed consistency filter is constructed to realize the real-time consistency estimation of the coordinates of the moving object at multiple points under the condition of multiple sensor nodes.
The invention has the advantages that: the influence of the actual multiple sensors is considered, a system state equation and an observation equation are established for the target model, a designed distributed consistency filter is provided, and real-time consistency estimation is carried out on the position of the moving target. The estimation result can meet the precision and real-time requirements of practical application, and the algorithm can be well matched no matter what target is used, so that the requirement of target tracking is met.
Claims (1)
1. A target tracking method based on distributed consistency filtering of a wireless sensor network comprises the following steps:
1) Establishing a continuous kinematic model for the motion condition of a moving target on the horizontal ground; establishing a horizontal ground environment into a plane rectangular coordinate system, and then using To represent the position of a moving object, where P x represents the abscissa of the object and P y represents the ordinate of the object;
2) Establishing a system state equation and an observation equation of each sensor node; according to the actual situation, a system state equation and an observation equation of each sensor node are established, and the method comprises the following steps:
(2.1) establishing a state equation of the system; the state equation of the system is:
x(k+1)＝Ax(k)+B0ω0(k) (1)
Wherein k represents the current discretization time, k+1 represents the next discretization time, the estimation target x represents the position of the object, x= [ P x Py]T,Px ] represents the abscissa of the object, P y represents the ordinate of the object, the superscript "T" represents the transpose of the matrix, a represents the state transition matrix of the estimation target x, ω 0 represents white noise with a mean value of 0 and a variance of 1, and B 0 represents the input matrix of white noise ω 0;
(2.2) establishing an observation equation for each sensor; the observation equation for the i-th sensor is:
zi(k)＝Hix(k)+D0;iω0(k) (2)
Wherein k represents the current discretization moment, z i represents the observation vector of the ith sensor, x represents the estimation target, H i represents the observation matrix of the estimation object of the ith sensor, ω 0 represents white noise with a mean value of 0 and a variance of 1, and D 0;i represents the observation matrix of the white noise ω 0 of the ith sensor;
3) Designing a corresponding distributed consistency filter according to the observed value of each sensor; assuming that N sensors are provided, each sensor is provided with a corresponding filter, and the definition eta represents a set of all the sensors, wherein eta is = {1, …, N }; in distributed hybrid filtering, for the ith filter, it can receive not only the observations z i (k) from its own sensor, but also the observations of its neighboring sensors Definition η i represents the set of adjacent observations received by the ith sensor; define J i as the i-th sensor itself and all its neighbors;
when a target is tracked, data transmission is performed in a wireless sensor network, and for an ith sensor, the ith sensor can receive the observation value of an adjacent sensor through the wireless sensor network, but the ith sensor can be disturbed in the transmission process, so that the data is lost; assuming that all observations actually received by the ith sensor are noted as:
where k represents the discretization time, Representing all data actually received by the ith sensor,/>All neighboring sensor observations/>, representing the ith sensorWhether the data transmitted to the ith sensor is lost;
designing a distributed consistency filter of each sensor:
Wherein k represents the current discretization time and k+1 represents the next discretization time; a represents a state transition matrix of the estimation object x, Represents the estimated value of the estimated object x, Σ represents the accumulated sign, e represents the belonging sign, L i represents the filter gain of the ith sensor, η i represents the set of adjacent observations received by the ith sensor, J i is the ith sensor itself and all its neighbors,/>All neighboring sensor observations/>, representing the ith sensorWhether data transmitted to the ith sensor is lost, Φ ij (k) represents whether data transmitted to the ith sensor by the neighbor sensor observation z j (k) of the ith sensor is lost, and/>Representing the set of all observation matrices of the ith sensor,/>Representing all data actually received by an ith sensor, wherein alpha is a to-be-determined consistency coefficient;
the function of the distributed consistency filter is to enable each sensor to estimate the target The convergence, realize the real-time consistency estimation to the moving target;
4) Giving a system autonomous error model and the gain of each filter, designing and solving a consistency coefficient through a matrix inequality; giving a system autonomous error model and the gain of each filter, designing and solving a consistency coefficient through matrix inequality, and specifically comprising the following steps:
(4.1) giving an autonomous error model of the system; the following autonomous error system models are obtained through the steps 1), 2) and 4) respectively:
Wherein k represents the current discrete time and k+1 represents the next discrete time; e i represents the estimation object x and the corresponding estimation value Sigma represents an accumulated sign, E represents a sign, L i represents a filter gain of an ith sensor, eta i represents a set of adjacent observations received by the ith sensor, A represents a state transition matrix of an estimation object, B 0 represents an input matrix of white noise omega 0, omega 0 represents white noise with a mean value of 0 and a variance of 1,/>Representing all neighboring sensor observations of the ith sensorWhether data transmitted to the ith sensor is lost, Φ ij (k) represents whether data transmitted to the ith sensor by the neighbor sensor observation z j (k) of the ith sensor is lost, and/>Representing the set of all observation matrices for the ith sensor,Representing a set of all white noise observation matrixes of the ith node, wherein alpha is a to-be-determined consistency coefficient;
(4.2) giving an expression of the filter gain L i; based on a system autonomous error model (5), an expression of a designed filter gain L i is given through a Kalman filtering algorithm:
Where k represents the current discretization time, a represents the state transition matrix of the estimation object, the superscript "-1" represents the inverse of the matrix, the superscript "T" represents the transpose of the matrix, B 0 represents the input matrix of white noise ω 0, Set of all observation matrices representing the ith node,/>Representing the set of all white noise observation matrices of the ith node,/>Representation/>O 0;i (k) and Λ i are both intermediate matrices;
(4.3) giving a diagonal matrix set form of intermediate variables O 0;i; intermediate variable O 0;i represents the covariance form of the autonomous system error model (5), i.e Given the diagonal matrix set form of intermediate variable O 0;i:
O0＝Diag{O0;i} (7)
Wherein, diag represents a diagonal matrix form, and O 0;i is an intermediate matrix;
(4.4) giving the initial value of the intermediate variable O 0; when k=0, an initial value is given to intermediate variable O 0, i.e
O0(0) (8)
(4.5) Giving the value of the consistency coefficient α; assigning a given value to a pending consistency coefficient alpha, i.e
α＝ε (9)
Wherein α is a coefficient of identity to be determined and ε represents a given value;
(4.6) giving a matrix inequality of the intermediate matrix O 0; the intermediate matrix O 0 satisfies the following matrix inequality:
Thus, an intermediate matrix O 0 (1) is obtained:
Where k represents the current discretization time, k+1 represents the next discretization time, the superscript "T" represents the transpose of the matrix, the superscript "2" represents the square of the value, mu ij represents the mathematical expectation of Φ ij, O 0 is the intermediate matrix, And/>All are intermediate matrixes related to alpha, and alpha is a to-be-determined consistency coefficient;
(4.7) solving the maximum value of the consistency coefficient alpha under the condition that all characteristic values of the intermediate matrix O 0 are larger than 0; repeating steps (4.5) and (4.6);
if k=t, all eigenvalues satisfying the matrix O 0 (T) are greater than 0, and the maximum value of the consistency coefficient α is solved, so as to obtain:
max(α)，eig{O0(T)}>0 (12)
Wherein alpha is a to-be-determined consistency coefficient, eig represents a characteristic value of the matrix, and O 0 is an intermediate matrix;
5) Substituting the consistency coefficient of the filter to obtain a real-time estimated value, and realizing the real-time consistency position tracking of each sensor on the moving target; substituting the solved consistency coefficient alpha into a distributed consistency filter formula (4) to realize real-time consistency estimation of each sensor node on the moving target x.
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